%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS115+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:59:43 PM UTC 2026
% Result : Unsatisfiable 0.01s 0.38s
% Output : CNFRefutation 0.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 71 ( 6 unt; 4 def)
% Number of atoms : 209 ( 17 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 235 ( 97 ~; 90 |; 33 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 111 ( 96 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf2(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] :
( cp1(X)
=> cp2xcomp(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] :
( cp2(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X] :
( cp2xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X] :
( cowlThing(X)
=> ! [Y0,Y1] :
( ( rf1(X,Y1)
& rf1(X,Y0) )
=> Y0 = Y1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X] :
( cowlThing(X)
=> ! [Y0,Y1] :
( ( rf2(X,Y1)
& rf2(X,Y0) )
=> Y0 = Y1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
cUnsatisfiable(i2003_11_14_17_21_30578),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] :
( rr(X,Y)
=> rf2(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X,Y] :
( rr(X,Y)
=> rf1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f77,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f83,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf2(X,Y) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf2(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f84,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf2(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ? [Y] :
( cowlThing(Y)
& rr(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf2(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf2(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cowlThing(sK2_skl(X))
& rr(X,sK2_skl(X))
& cp1(sK1_skl(X))
& rf1(X,sK1_skl(X))
& cp2(sK0_skl(X))
& rf2(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X)),skolemize(Y,sK2_skl(X))],[f84]) ).
fof(f86,plain,
! [X0] :
( rf2(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0] :
( cp2(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0] :
( rf1(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f89,plain,
! [X0] :
( cp1(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
! [X0] :
( rr(X0,sK2_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f93,plain,
! [X] :
( cp2xcomp(X)
| ~ cp1(X) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f94,plain,
! [X0] :
( cp2xcomp(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
! [X] :
( cp2(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f96,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp2(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp2(X) ) ),
inference(NNF_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp2(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp2(X) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
( ! [X] :
( ra_Px1(X,sK3_skl(X))
| cp2(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp2(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp2xcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cp2xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f102,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cp2xcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cp2xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cp2xcomp(X) )
& ! [X] :
( ra_Px1(X,sK4_skl(X))
| ~ cp2xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y0,sK4_skl(X))],[f102]) ).
fof(f104,plain,
! [X0] :
( ra_Px1(X0,sK4_skl(X0))
| ~ cp2xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f106,plain,
! [X] :
( ! [Y0,Y1] :
( Y0 = Y1
| ~ rf1(X,Y1)
| ~ rf1(X,Y0) )
| ~ cowlThing(X) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f107,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X2)
| ~ rf1(X0,X1)
| ~ cowlThing(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [X] :
( ! [Y0,Y1] :
( Y0 = Y1
| ~ rf2(X,Y1)
| ~ rf2(X,Y0) )
| ~ cowlThing(X) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f109,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X2)
| ~ rf2(X0,X1)
| ~ cowlThing(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
cUnsatisfiable(i2003_11_14_17_21_30578),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f111,plain,
! [X,Y] :
( rf2(X,Y)
| ~ rr(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f112,plain,
! [X0,X1] :
( rf2(X0,X1)
| ~ rr(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [X,Y] :
( rf1(X,Y)
| ~ rr(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f114,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rr(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f116,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X2)
| ~ rf1(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f77]) ).
fof(f117,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X2)
| ~ rf2(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f77]) ).
fof(f118,plain,
! [X0] :
( ~ cp1(X0)
| ra_Px1(X0,sK4_skl(X0)) ),
inference(resolution,[status(thm)],[f104,f94]) ).
fof(f119,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| X1 = sK1_skl(X0)
| ~ rf1(X0,X1) ),
inference(resolution,[status(thm)],[f116,f88]) ).
fof(f120,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| X1 = sK0_skl(X0)
| ~ rf2(X0,X1) ),
inference(resolution,[status(thm)],[f117,f86]) ).
fof(f121,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rf2(X0,sK2_skl(X0)) ),
inference(resolution,[status(thm)],[f112,f90]) ).
fof(f122,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rf1(X0,sK2_skl(X0)) ),
inference(resolution,[status(thm)],[f114,f90]) ).
fof(f123,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ra_Px1(sK1_skl(X0),sK4_skl(sK1_skl(X0))) ),
inference(resolution,[status(thm)],[f118,f89]) ).
fof(f126,plain,
! [X0] :
( X0 = sK0_skl(i2003_11_14_17_21_30578)
| ~ rf2(i2003_11_14_17_21_30578,X0) ),
inference(resolution,[status(thm)],[f120,f110]) ).
fof(f128,plain,
rf1(i2003_11_14_17_21_30578,sK2_skl(i2003_11_14_17_21_30578)),
inference(resolution,[status(thm)],[f122,f110]) ).
fof(f131,plain,
! [X0] :
( ~ cp2(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f123,f99]) ).
fof(f134,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_30578)
| sK2_skl(i2003_11_14_17_21_30578) = sK0_skl(i2003_11_14_17_21_30578) ),
inference(resolution,[status(thm)],[f126,f121]) ).
fof(f136,definition,
( sQ0_spl
<=> sK2_skl(i2003_11_14_17_21_30578) = sK0_skl(i2003_11_14_17_21_30578) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ0_spl
| sK2_skl(i2003_11_14_17_21_30578) = sK0_skl(i2003_11_14_17_21_30578) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
( sQ1_spl
<=> cUnsatisfiable(i2003_11_14_17_21_30578) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( sQ1_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_30578) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f134,f136,f139]) ).
fof(f147,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f110]) ).
fof(f148,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( ~ sQ0_spl
| rf1(i2003_11_14_17_21_30578,sK0_skl(i2003_11_14_17_21_30578)) ),
inference(backward_demodulation,[status(thm)],[f137,f128]) ).
fof(f154,plain,
( ~ sQ0_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_30578)
| sK0_skl(i2003_11_14_17_21_30578) = sK1_skl(i2003_11_14_17_21_30578) ),
inference(resolution,[status(thm)],[f150,f119]) ).
fof(f156,definition,
( sQ3_spl
<=> sK0_skl(i2003_11_14_17_21_30578) = sK1_skl(i2003_11_14_17_21_30578) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ3_spl
| sK0_skl(i2003_11_14_17_21_30578) = sK1_skl(i2003_11_14_17_21_30578) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f154,f156,f139,f136]) ).
fof(f171,plain,
( ~ sQ3_spl
| ~ cp2(sK0_skl(i2003_11_14_17_21_30578))
| ~ cUnsatisfiable(i2003_11_14_17_21_30578) ),
inference(paramodulation,[status(thm)],[f157,f131]) ).
fof(f177,definition,
( sQ6_spl
<=> cp2(sK0_skl(i2003_11_14_17_21_30578)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ6_spl
| ~ cp2(sK0_skl(i2003_11_14_17_21_30578)) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f171,f139,f177,f156]) ).
fof(f203,plain,
( sQ6_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_30578) ),
inference(resolution,[status(thm)],[f179,f87]) ).
fof(f205,plain,
( sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f203,f139,f177]) ).
fof(f206,plain,
$false,
inference(sat_refutation,[status(thm)],[f142,f148,f159,f180,f205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS115+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n006.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 22:53:44 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 % Drodi V4.1.1
% 0.01/0.38 % Refutation found
% 0.01/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.01/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.01/0.39 % Elapsed time: 0.032478 seconds
% 0.01/0.39 % CPU time: 0.076614 seconds
% 0.01/0.39 % Total memory used: 2.710 MB
% 0.01/0.39 % Net memory used: 2.634 MB
%------------------------------------------------------------------------------